\newproblem{lay:4_5_27}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.5.27}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Explain why the space $\mathbb{P}$ of all polynomials is an infinite-dimensional space.
}{
  % Solution
	Let us assume that $\mathbb{P}$ is finite-dimensional and that its dimension is $n$. Consider the set of polynomials of degree $n$ ($\mathbb{P}_n$). This obviously
	a subset of $\mathbb{P}$ so the dimension of $\mathbb{P}$ is larger than the dimension of $\mathbb{P}_n$
	\begin{center}
		$\mathbb{P}_n \subset \mathbb{P} \Rightarrow \mathrm{dim}\{\mathbb{P}_n\}<\mathrm{dim}\{\mathbb{P}\}$
	\end{center}
	The dimension of $\mathbb{P}_n$ is $n+1$, but $n+1>n$ so this is a contradiction with our hypothesis, and $\mathbb{P}$ is an infinite-dimensional space.
}
\useproblem{lay:4_5_27}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
